0.9999999 = 1

The thing I don't get is...

1.000000... = 0.99999999... ?

The numbers are clearly different so how can they be the same. They are as close to each other as can be, but still it's different. Every digit of those two numbers are not the same. The first digit 1 is not equal to 0, and all those 0's don't equal to those 9's.... *confused*

It's basically the same thing as Zeno's Paradoxes. No, 0.99999... never reaches 1 if you think of it finitely, but because it keeps going infinitely, the two numbers become the same.

Doesn't matter that the digits are different. 999 is one less than 1,000. 9,999 is one less than 10,000. The paradox results from a weakness in the decimal system that only calculus can eliminate.